Neural Contextual Bandits without Regret

TL;DR

This paper introduces neural network algorithms for contextual bandits, providing the first regret bounds for general contexts and demonstrating convergence rates under broad assumptions.

Contribution

It develops neural network-based algorithms with provable sublinear regret bounds for contextual bandits with general context sequences.

Findings

Bounded regret for NTK-UCB using NTK information gain.

Neural network algorithm NN-UCB closely tracks NTK-UCB's regret.

Achieved convergence to optimal policy at rate .5d}

Abstract

Contextual bandits are a rich model for sequential decision making given side information, with important applications, e.g., in recommender systems. We propose novel algorithms for contextual bandits harnessing neural networks to approximate the unknown reward function. We resolve the open problem of proving sublinear regret bounds in this setting for general context sequences, considering both fully-connected and convolutional networks. To this end, we first analyze NTK-UCB, a kernelized bandit optimization algorithm employing the Neural Tangent Kernel (NTK), and bound its regret in terms of the NTK maximum information gain $\gamma_T$, a complexity parameter capturing the difficulty of learning. Our bounds on $\gamma_T$ for the NTK may be of independent interest. We then introduce our neural network based algorithm NN-UCB, and show that its regret closely tracks that of NTK-UCB. Under broad non-parametric assumptions about the reward function, our approach converges to the optimal policy at a $\tilde{\mathcal{O}}(T^{-1/2d})$ rate, where $d$ is the dimension of the context.